The grades on a physics midterm at Covington are normally distributed with $\mu = 78$ and $\sigma = 3.5$. William earned a $68$ on the exam. Find the z-score for William's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for William's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{68 - {78}}{{3.5}}} $ ${ z \approx -2.86}$ The z-score is $-2.86$. In other words, William's score was $2.86$ standard deviations below the mean.